Gradient index light conductor

ABSTRACT

Novel optical lens elements are disclosed, each of said elements consisting of a transparent body having two end surfaces crossing its center axis and having a refractive index distribution capable of substantially satifying the following relation.

United Stat- 52 4 [111 3,801,181

Kitano et al. I 1 Apr. 2, 1974 [541 GRADIENT INDEX LIGHT CONDUCTOR Wood, Physical Optics, 2nd Edition, Published in [75] Inventors: Ichiro Kitano, Kobe; Ken Koizumi, I911 1 86*91 ltami; flimyoshi Matsumun, Osaka; Kawakami et 211., Article in Proceedings of the IEEE Kunihiko Mukai, Tsu; Teiji Uchida, 2148-2149 1965- Tokyo, all of Japan Primary Examiner-David l-l. Rubin Assign: l-P Self Kabushiki Kaisha Attorney, Agent, or Firm-Robert E. Burns; Emman- Tokyo-to, Japan uel J. Loboto [22] Filed: Dec. 7,- 1971 [57] ABSTRACT PP 205,667 Novel optical lens elements are disclosed, each of said Related Appncation Data elements consisting of a transparent body having two end surfaces crossing its center axis and having a re- 63 Continuation of Ser. Nov 848,471, Au 8, 1969, 1 g fractrve index distribution capable of substantlally satiabandoned.

fying the. following relation. [30] Foreign Application Priority Data n N (1 i a r Aug. 10, 1968 Japan 43-56968 where N represents its refractive index at a point on Aug. 21, 1968 Japan 1. 43-60097 the enter axis on a sectional area perpendicular to g- I968 Japan 098 said center axis, n represents its refractive index at a g- 1968 Japan r 4360099 radial point at a distance r from the former point, and Aug. 21, 1968 Japan 43-60100 4 represents a positive constant. Sept. 26, l968 Japan 43-70075 Furthermore, various applications of the above-mentioned optical lens elements are disclosed,

[52] U.S. Cl. 350/96 R, 350/96 WG, 350/175 GN Sm [5 Int Clinstruments Such exam 1 fibersco 5 made f 581 Field of Search 350/96 R, 96 B, 96 we, combinations of the optical) g an 350/175 GN optical fiber bundle, a compound gpt igal lens consistin of a luralit of tlie E tical lens elemnts [56] Rdnnces (med which ar e paral felly ar ranged, f rfiimr'n'e'fi't' UNITED STATES PATENTS madefiflmmm and 3,614,197 10/1971 Nishizawa et al. 350/96 WG a photosensitive layer, an image transmission optical 3,320,] l4 5/l967 Schulz 350/96 R X device having a high resolution and being very easy in 3,434,774 3/1969 Miller 350/96 WG the handling and preservation, a view finder, and OTHER PUBLICATIONS various light-beam transmitting conducters and their Miller, Article in Bell System Technical Journal, Vol. connection pans 44, No. 9, Nov. 1965, pgs. 20l72030 cited. 3 Claims, 62 Drawing Figures MENTEBAPR 2 I974 SHEET 01 W12 FIG.

.AIENTEDAPR 2 I974 3,801,181

SEE! 03ff12 FIG. ll

J--- 3 fi L6 F|G.l2

30,5 a 20u E02 6 LENGTH OF LENS (mm) PMENTEDAPR 2:914 3.801.181 sneer 0u0F12 PATENTEDAPR 2 m4 sum 05 M12 LENGTH OF LENS H FIG.I9

FIG. 20(8) DATENTEUAPR 2mm 3.801.181

sum us'nr12 FIG. 4| l b FIG. 43 B RADIUS (mm) 50 I00 LENGTH OF LENS (cm) PATENTEHAPR 21914 SHEET 0711f 12 PATENTEDAPR 2 m4 sum 11 [1F 12 FIG. 46

FIG. 47 FIG. 48

PATENTEDAPR 2mm 3Q801l8l sum 12 nr 12 i "d; i F6} 5 z i i L Lr I o I r 3% F I G. 57 2 0.5- E I O.l i

0 i '2 a 9 IO LENGTH OF LENS(Z) m) FIG. 58 F 7 76 75 FIG. 59

BACKGROUND OF THE INVENTION A fiberscope consists fundamentally of a bundle of optical fibers arranged in such a manner that the fibers are disposed in the same order at both ends, and an objective and ocular lens provided respectively at two ends of the bundle. An image of an object to be ob served is formed at one end of the bundle of the optical fibers by means of the object and the same image is transmitted to the other end of the bundle of the optical fibers. This image is viewed directly with the naked eye or led to a recording device through an ocular lens. When such a fiberscope is utilized as a borescope to be inserted into somatic cavities for observation, its diameter is often required to be as small as possible. However, primarily because the production of objectives with a small diameter involves much difficulty, fiberscopes having a small diameter, such as those with a diameter of their image transmitting portion or their effective diameter of less than 1 mm., have conventionally been unobtainable. For, in spite of the fact that the objectives of prior fiberscopes must have their surfaces ground into definite curvatures, a high degree of precision in such grinding operation could not be obtained in the case of lenses having a small diameter, so that the production of small-diameter lenses having a practically applicable degree of resolving power, for instance those with a diameter of less than l mm., could not be expected. Furthermore, in the conventional fiber scopes, the side field of an object cannot be effectively viewed. In this invention, improved lens elements adapted for the manufacture of fiberscopes not having the disadvantages described above are proposed.

Still further, conventionally, an optical lens consisting of a solid transparent substance such as glass and synthetic resin and being curved at least one of its opposed two faces has been well known. The principle of such a lens is the utilization of light refraction at the curved face which is an interface between two substances having different refractive indexes. The shape of the curved face can determine such optical characteristics of a lens as the local distance, aberration and the like. Ordinarily, the faces of lenses are finished with definite curvatures by grinding and other finishing means, but the production of a lens with a small aberration requires a precision-made surface finishing apparatus and skilled operation thereof. Especially, in the surface finishing of lenses with a small aperture, such as those having an aperture of less than several millimeters, it is extremely difficult to obtain the desired degree of precision by conventional grinding and other finishing machines, so that small-aperture lenses are made exclusively on the basis of manual production and, even then, those with small aberration have not been easily obtained. V

When a gas is caused to flow in a laminar flow within a pipe from one end thereof to the other and the wall of the pipe is heated, the gas in the pipe has such a distribution of refractive indices that it is decreased nearly in proportion with the square of the distance from the center axis of the pipe, said gas having an image forming action like that of a convex lens. This phenomenon is known as the so-called principle of a gas lens, as is described, for instance, in pp. l80l87 of No. 36, Vol.

3, of a magazine Oyo Butsuri (Applied Physics). Thus a gas lens capable of functioning as a concave lens can be obtained. However, this gas lens has a number of drawbacks in that it requires the application of external power, is inferior in resolving power, and cannot be reduced to the size of miniature lens; and thus it is not applicable for practical use. Miniature optical lens elements not having the disadvantages of the conventional lens elements are proposed in this invention. On the other hand, various problems for obtaining an extremely small recording element adapted to effectively and simply reproduce any record without necessitating a view finder, an image transmission device having a high resolution, an effective view finder an effective light-beam transmitting long and this conducter, and effective connection parts for said device and conducter could not be easily solved merely by the concept of the conventional optical lens elements. These problems also have been solved in this invention.

SUMMARY OF THE INVENTION A first object of the invention is to provide an object lens element having a predetermined refractive index distribution established by continuous variation of its refractive index on the internal portion thereof and adapted to manufacture various optical instruments such as fiberscopes, compound lens elements, and optical transmission devices.

A second object of the invention is to provide a miniature optical lens element the aberration of which is caused to be very small without necessitating any curvature finishing of its surface.

A third object of the invention is to provide excellent and miniature fiberscopes not accompanied by the disadvantages of conventional fiberscopes.

A fourth object of the invention is to provide excellent and miniature fiberscopes enabling effective viewing of the side field of an object.

A fifth object of the invention is to provide a novel recording element which can reproduce any record in a simple, accurate and magnified manner without necessitating any view finder.

A sixth object of the invention is to provide an image transmission device which has high resolution ability, is easy in its preservation and handling and is free in vibration and bending of the tr transmission passage of said device and its position of image convertor of said device.

A seventh object of the invention is to provide an improved lens element having a large input or output surface, said element being a conductor having at least one end capable of making any light-beam to be easily incident.

A eighth object of the invention is to provide effective connection parts of a light-beam transmitting device.

The above objects and other objects of the invention have been attained by basically utilizing a novel optical lens element consisting of a transparent body having two end surfaces crossing its center axis and having a refractive index distribution capable of substantially satisfying the following relation.

where N represents its refractive index at a point on the center axis on a sectional area perpendicular to said center axis, n represents its refractive index at a radial point at a distance r from the former point, and (a) represents a positive constant.

The present invention is .based on the fact that glasses, synthetic resins and other solid transparent substances having the above-described refractive index distribution can function as any lens or any composite lens and sufficiently stand practical use. That is, the invention utilizes a principle such that when a light wave progresses through a transparent body having a refractive index gradient varying in a direction crossing the light progressing axis, the light progresses while varying its path toward the direction of higher refractive index.

The objects and various characteristic features of the invention will be described in detail in conjunction with the drawings, in which the same or equivalent members are designated by the same reference numerals and characters.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a view showing the principal relation between an object and its image in the optical lens element according to the invention;

FIG. 2 is a sectional view showing an example of a fiberscope according to the invention;

FIGS. 3, 4, 5, 6, 7 and 8 are, respectively, views showing various relations between an object and its image in the optical lens element according to the invention;

FIG. 9 is a view showing a fiberscope in which a curved optical lens element is utilized;

FIG. 10 is a perspective view of the curved optical lens element shown in FIG. 9;

FIG. 11 is a partial view of a curved optical lens element according to the invention in which a light-beam transmitting manner is shown;

FIG. 12 is an experimental characteristic curve showing relation between the radius and length of optical lens elements manufactured according to the invention;

FIG. 13 is a schematic view showing other fiberscope manufactured according to the invention;

FIG. 14 is a view showing another principal relation between an object and its image in the optical lens element according to the invention;

FIG. 15 is a graphic view showing the relation between focus distance and lens length of the optical lens element shown in FIG. 14;

FIG. 16 is a view showing the relation between an object and its image in the optical lens element shown in FIG. 14;

FIG. 17 is a view for showing FIG. 5 in a more detailed manner;

FIG. 18 is a graphic view showing the relation between focus distance and lens length of the optical lens element shown in FIG. 17;

FIG. 19 is a view showing the relation between an object and its image in the case where the optical lens element illustrated in FIG. 17 is used;

FIG. 20 (A) is a view showing in detail a part of a curved lens element according to me invention;

FIG. 20 (B) is a view showing light-beam transmission in an optical lens element according to the invention, said element having a curved center axis;

FIG. 21 is a view showing light-beam transmitting in an optical lens element according to the invention, said element having the coefficient (a) which varies along the center axis of said element;

FIGS. 22, 23, and 24 are graphic views showing internal refractive index distributions at the sectional areas along planes 22A-22B, 23A-23B, and 24B, respectively;

FIG. 25 is a view showing an example of the optical lens element'according to the invention;

FIG. 26 is a graphic view showing the refractive index distribution at a sectional area of the optical lens element illustrated in FIG. 25;

FIG. 27 is a view showing the relatidn between an object and its image in other example of the optical lens element according to the invention;

FIG. 28 is a schematic view showing a microscope in which an optical lens element according to the invention is applied;

FIG. 29 is a schematic view, partly in section, showing another improved fiberscope according to the invention;

FIG. 30 is a perspective view showing a divided head portion of the fiberscope illustrated in FIG. 29;

FIG. 31 is a view showing the relation between an object and its image in the fiberscope illustrated in FIG. 29;

FIGS. 32 (A and B) is a perspective view showing a principal structure of a recording element according to the invention;

FIG. 33 is a schematic view, in vertical section, showing a micro-camera in which the recording element illustrated in FIG. 32 is utilized;

FIG. 34 is a schematic view, in vertical section along length-wise direction, showing a principal part of a camera adapted to photograph internal organs of a human body, in which a recording element according to the invention is utilized;

FIG. 35 is a schematic view showing an example of an image transmission device according to the invention;

FIG. 36 is a schematic view, in section, showing a view finder which functions as an image transmitting part of an image transmission device according to the invention;

' FIG. 37 is a view of schematic optical system of the view finder illustrated in FIG. 36;

FIG. 38 is a view, partly in section, showing a modified view finder to be used, in combination with the image transmission device according to the invention;

FIG. 39 is a view of schematic optical system of the view finder illustrated in FIG. 38;

FIG. 40 is a view, partly in section, showing a modification of the view finder illustrated in FIG. 38;

FIG. 41 is a view showing schematic optical system of the view finder illustrated in FIG. 40;

FIG. 42 is a view showing schematic optical system of other view finder which is used in combination with an image transmission device according to the invention;

FIG. 43 is a view showing relation between radius and length of a fiber glass body according to the invention and used in the view finder illustrated in FIG. 42;

FIG. 44 (A) is a schematic view for showing an example according to the invention, in which the input end surface is enlarged;

FIG. 44 (B) is a schematic view forshowing a modification of the example of FIG. 44 (A);

FIG. 45 is a schematic view showing a conventional case corresponding to the example shown in FIG. 44 (A) or FIG. 44 (B);

FIG. 46 is a schematic view of a light-beam transmitting conductor according to the invention;

FIGS. (47, 50), (48, 51) and (49,52) show various refractive index characteristics at end surface 5,, sectional planes (S S and (S S in FIG. 46, respectively;

FIG. 53 is a schematic view of a modification of the conductor shown in FIG. 46;

FIGS. 54, 55 and 56 show, respectively, refractive index characteristics at end surface S and sectional planes (5-, S70) and S S in FIG. 53;

FIG. 57 is a view showing relation between radius and length of a glass body according to the invention;

FIG. 58 is a schematic view showing connection part of two lightbeam transmitting conductors according to the invention; and

FIG. 59 is a schematic view showing a modification of the connection part illustrated in FIG. 58;

DETAILED DESCRIPTION OF THE INVENTION Glasses, synthetic resins and the like are most suitable as material for the solid transparent substance having the mentioned refractive index distribution represented by the equation n N (l ar Especially, in the case of a glass, a desired refractive index distribution can be obtained easily by gradually varying the refractive indexes in the interior of the glass by regulating the concentration of cations composing the glass, as is described in the Japanese Pat. No. SHO 43-16986 which corresponds to US. Pat. application Ser. No. 806,368 which is now abandoned in favor of continuation application Ser. No. 147,256. In the case of synthetic resin, such a refractive index distribution can be obtained by covering a resinous core member with several kinds of synthetic resins having different refractive indexes, subjecting said covered product to a diffusion at a high temperature and thereafter applying heat thereto to obtain a consecutive variation in the refractive indexes of the resins.

The lens element according to the present invention is equipped with functions of a lens if its refractive index distribution roughly satisfies the above equation. Even when terms such as r and r are present in the brackets in the right member of said equation, the functioning of the lens element as a lens is not influenced if their coefficients are small.

The following description relates to the case in which the refractive index distribution n N (l ar) is adopted.

Now, calculations as to the positions and sizes of images formed by a lens made of a transparent substance having the above refractive index distribution are given below. In FIG. 1, the reference numeral 1 designates a columnar lens having a radius R, a length 2, and a refractive index distribution n N 1 ar), where or I while the reference numeral 2 represents a transparent substance closely attached to the lens I and having a diameter R, a length t and a uniform refractive index n,,. Relative expressions of paraxial rays are given below when an object p is placed at a position at a distance 1 from a position at a front plane of the lens I and, consequently, a real image is formed at a rear plane 0,, of the transparent substance 2. Rays A entering the lens from its upper end at the position 0 and in parallel with the optical axis of the lens I, and rays B passing the position at the optical axis of Q from the same start point as the rays A are pursued to obtain their crosspoint.

When the position of the rays A from the optical axis in the lens at 0,, is X, and angle of the rays A at A,, is taken as 8,, a matrix of rays at Q is:

X |:cos #571; 1 sin {27: R SA sin El {t Ta cos m] [O] [R cos 1 4am sin v55 when the position of the rays A in the transparent substance 2 at Q is X M and its angle is S X Rcosm s.]= A i ismmt Therefore, the position X of the rays A at Q, is:

When the position of the rays B in the lens I at Q, is X B and its angle is S When the position of the rays B in the transparent substance 2 at 0,, is X and its angle is S Therefore the position X of the rays at Q, is:

X -(R/n,,l) t cos V 2a t (R/n l 2a) sin V 2a t (2) If the expression (1) and expression (2) are equal:

1 1 Nt m cos /Zt+n. sin v55:

Ka sin 55133 1552927 The size X of the image at Q, is obtainable by substituting the equation (3) into the equation (I).

An end surface of a bundle of optical fibers of the fiberscope is closely attached to the rear plane of the transparent substance 2. When the bundle of optical fibers is directly attached to the lens I, I, in the equation (3) may be replaced by O. A condition for an image of an object being infinitely far is obtained by substituting the denominators of the right member of the equation (3), as follows:

When the transparent substance 2 is composed of air and other fluids, a distance from an object as well as magnification can be adjusted easily by optionally varying the length t of the transparent substance. Also, in case there is need for lessening the reflection loss of light at an interface between the transparent substance 2 and lens 1 and at an interface between the transparent substance 2 and the bundle of optical fibers, the refractive index of the transparent substance 2 may approximated to those of the lens I and the bundle of optical fibers or, dispensing with the transparent substance 2, the lens I and the bundle of optical fibers may be closely attached to each other.

In the case of closely attaching the lens to the bundle of optical fibers, it has been confirmed that favorable length of the lens is within the range between [(ml)1r 'fi'rr/ 2a] and [(ml)1r 5/61r/ 2a], where m represents a positive integer.

According to the present invention, the surface of objectives used in fiberscopes need not be ground into definite curves, so that lens having both a small diameter and a superior resolution ability are obtainable. Thus, a fiberscope of a small diameter can be materialized and utilized as a borescope and the like to be inserted into narrow cavities for observation.

The following examples 1 to 6 relate, respectively, to the cases in which the lens element according to the invention is applied to a fiberscope.

Example 1 A bar of glass with a diameter of 0.08 cm. and composed of wt. percent of T1 0, 12 wt. percent of Na 0, 20 wt. percent of PbO and 48 wt. percent of SiO was immersed in a bath of potassium nitrate at a high temperature for a prescribed length of time, whereby a glass bar showing a center refractive index n of 1.60, a surface refractive index of 1.57 and an internal refractive index distribution nearly satisfying the equation n N (l ar) was obtained, in said equation r is the distance from a center and a 11.7 cm". This bar was cut and both of its ends were ground so as to be at a right angle to the bar, whereby to obtain a first glass bar with a length of 0.250 cm. Separately therefrom, a

second glass bar having both of its ends ground was prepared and had a refractive index of 1.70, a diameter of 0.08 cm., and a length of 0.099 cm. This second. bar was attached to one end of a bundle of optical fibers of a fiberscope with a diameter of 0.08 cm., and, further, the first bar was attached thereto as illustrated in FIG. 2, to complete an objective portion of the fiberscope. In the drawing, reference numeral 3 designates the first glass bar,4 the second glass bar, 5 the bundle of optical fibers, and 6 protective film. This optical system is illustrated in FIG. 3.

When this fiberscope was employed for actual observation, a range C surrounded by a circle with a diameter of 1 cm. of an object approx. 2 cm. in front of the leading end of the fiberscope was clearly observable. In this instance, an inverted real image D is formed at the end of the optical fiber bundle on the side of the objective.

Example 2.

As illustrated in FIGS. 4 and 5, a glass bar 7 which is the same as the first glass bar in Example I was placed at an adjustable distance from the end of the bundle of optical fibers 8. According to this fiberscope, a scope with a diameter of 1.6 cm. of an object (P) 2 cm. away was observed clearly when the mentioned distance was set to 0.058 cm. as shown in FIG. 4. When the distance was adjusted to 0.069 cm. as in FIG. 5, a scope with a diameter of 0.5 cm. of an object 1 cm. away was viewed clearly. In either case, the inverted real image (Q) of the object was formed at the end of the bundle of the optical fibers on the side of the objective.

Example 3 A bar of glass having a diameter of 0.02 cm., a center refractive index of 1.60, a surface refractive index of 1.57, aiid an ifiternal'refractive index 'distributiohsatisfying the equation n n (1 ar where a 1.88 X 10 cm. was prepared according to the processing analogous to that in Example 1. In cutting out a lens from this bar, a condition for obtaining the shortest focal distance, that is, the smallest t in:

sin V2at =l Example 4 our (Ya grasses; inat'eFaTtiaViiig' meter of 0108 cm., a center refractive index n. of 1.60, a surface refractive index of 1.57, and an internal refractive index distribution satisfying the equation n n (1 ar), where a 11.7 cm", a glass bar 11 with a length of 0.378 cm. and having both ends ground perpendicularly to the bar was produced, as illustrated in FIG. 7. When this glass bar as an objective was attached to the end 12 of a bundle of optical fibers, a scope with a diameter of 0.3 cm. of an object (P) 0.5 cm. away could be seen clearly. In this case, too, an inverted real image (Q) was formed at the end of the bundle of optical fibers. Then, as shown in FIG. 8, a glass bar 13 with a length of 1.026 cm. was produced from the above material in the same way and attached to the end 14 of a bundle of optical fibers, then a range with a diameter of 0.3 cm. of an object (P) 0.5 cm. away could be observed clearly as in the former example, with only a dif ference such that an erect real image (Q) was formed at the end of the fiber bundle.

Example 5 A bar of glass with a diameter of 0.6 mm. and consisting of 48 wt. percent of SiO,, 12 wt. percent of T1 0 and 20 wt. percent of PhD was prepared and immersed in a bath of potassium nitrate at a temperature of 480C for hours. The glass bar extracted therefrom was heated up to a temperature of 520C and curved with a curvature radius of 1 mm. (to a center axis). The bar was then maintained at a temperature of 450C for 10 hours to remove its internal stress. This bar showed a center refractive index N of 1.60, a surface refractive index of 1.52, and an internal refractive index distribution n nearly satisfying the equation n N (l ar where a 0.56 mm? This bar was finished into such a shape that its length at the center axis is 20 mm. and its end faces are perpendicular to the center axis. As illustrated in FIG. 9, the objective [5 thus obtained was attached to an end of a bundle of optical fibers 16. The light beam due to an object P placed at a definite position obliquely in front of one end of the objective 15 had formed a real image Q at an end of the fiber bundle. FIG. plots the external view of the objective 15.

The relation between an objectand image in case the center axis of the objective is curved as in the foregoing is absolutely the same as the equation (3) established previously with respect to a straight center axis. However, an optical axis is not in agreement with the center axis of the lens element, but is deviated outwardly therefrom by a distance equal to (2au)", where u is a curvature radius at the center axis of the lens element. In FIG. 9, h designates the center axis of the lens as well as its extension while chain line j represents the optical axis and its extension.

As illustrated in FIG. 11, light beam b in the interior of a lens 15a having a curved center axis wanders about its optical axis j. When a shift between an optical axis and center axis, e.g., (2au)", is considerably short as compaed with the radius R of the lens, the light beam can wander or oscillate about the optical axis no matt how long the lens may be, so that an image is transmitted. On the other hand, when (2au)' is approximately the same as or greater than R, the light beam wandering about the optical axis is emitted out of the lens from the periphery thereof, so that length of the lens has to be less than 1r (2a).

Example 6 Glass consisting of 48 wt. percent of SiO,, 12 wt. percent of Na O, wt. percent of T1 0 and 20 wt. percent of PbO was melted in a temperature range of 900950C and extracted at a regulated speed and the a glass substance thus obtained possessed a radii characteristic as shown in FIG. 12. The glass substance was cooled gradually to remove its stress and thereafter immersed in a bath of KNO maintained at a temperatures of 460C. The glass substance was then extracted out of the bath at a regulated speed. The refractive indexes in a cross section of the glass substance thus obtained are distributed in such a manner than (a) is decreased at a certain rate with an increase in diameter and the resulting product was used as an objective in a fiberscope. In FIG. 13, the reference numeral 17 designates an objective obtained in the way described above, 18 a bundle of optical fibers arranged in the same order at both ends thereof, and 19 a glass substance having a refractive index close to those of the objective l7 and bundle of optical fibers 18. A protection glass 20 is provided outside the objective 17. Light led from a light source 21 through a light guide member 22 consisting of a bundle of glass fibers is radiated onto an object 23 to be observed. An image of the object 23 is formed at one end of the bundle of optical fibers l8 bythe objective l7, and the same image is transmitted to the other end of the bundle of optical fibers 18. This image is either observed with the naked eye or led to a recording device and the like through an ocular lens 24. According to the present invention, a light-beam which enters through the objective I7 is gradually enlarged in amplitude, so that an image formed at one end of the optical fiber bundle 18 is magnified and superior in resolution. Thus the fiberscope of this invention is suited for the observation of minute portions such as the interiors of somatic cavities.

The following description relates to the case in which the refractive index distribution n N (I ar is adopted.

Now, when the constant (a) is invariable in any cross section, the center axis is straight, and both ends are in a plane perpendicular to the center axis, the relationship between an object and its image in an optical system employing the lens element according to this invention is as follows. in FIG. 14, the reference numeral 1 designates a columnar lens, having a radius R, a length l, and a refractive index distribution n N (I 111? where ar l The focal distance f of this columnar lens 1 can be obtained in the same way as that of an analysis as applied to a medium having the above refractive index distribution which is described in pp. 465-467 in the thesis of H. Kogelnik carried in pp. 455-494 of the March, 1965, issue of the Bell system Technical Journal, published in the USA.

More specifically, the focal distance f can be obtained by the following equation, when (2a)"""= C:

f= (NC sinh ct) (5) However, the focal distance f is represented either by the distance measured toward a space on the side of an object from a first principal point of the lens or the distance measured toward a space on the side of an image from a second principal point. The distance h of a corresponding principal plane H, or H as measured inwardly from the end faces of the lens is represented by:

h (NC) tanh A ct In FIG. 14, F1 and F2, respectively, designate the positions of focal points on the sides of the object and image, while H1 and H2 represent principal planes on the sides of the object and image.

When an object P is placed in a space on the side of the object at a distance k from the principal plane H1, an image 0 is formed at a position in a space on the image side at a distance I from the principal plane H2. In this case, paraxial light-beams are such that the equation:

is established between the distance k of the object and the distance I of the image, in the same way as in an ordinary lens formula.

Equation (5) of the focal distance and equation (6) of the principle plane distance h are represented in FIG. 15 as functions of the length of the lens, where the axis of the abscissa represents the length of the lens while the axis of ordinates represents the focal distance and principal plane distance. The full line designates the f focal distance f and the chain line represents the principal plane distance h. The focal distance is varied from negative infinity to zero along with increase in the length of the lens. And the principal plane distance is varied from zero to (NC) along with increase in the length of the lens. Therefore, when, for instance, the principal plane and focal point on the side of the image are considered, the principal plane on the side of the image is always placed inwardly from the end face on the side of the lens irrespective of the length thereof, while the focal point on the side of the image is always placed inwardly from the end face on the side of image and farther than the principal plane on the side of the image.

FIG. 16 plots variation of image position in the case of changing position of the object. When the object is moved from P1, P2 to P3 in the drawing, its image due to the lens I is changed from Q1, O2 to Q3. The parallel light beams from the object side said light beams being, are dispersed, but when said light beams are extended in the opposite direction, they are converted at one point at the position of F2. The parallel light beams from the image side also form their focal point at Fl at a position symmetrical to F2 with respect to the lens. When the object moves toward P3 from P1, an erect virtual image is formed which is gradually enlarged from O1 to Q3.

Now, in FIG. 16, the variation of an image is considered as the length of the lens is varied. In this case, F2 is moved in the right hand direction and F1 in the left hand direction when length of the lens is made greater, so that the image always appears as an erect virtual image though it decrease in size thereof.

Two end faces of the lens according to the present invention ordinarily have planes perpendicular to the center axis thereof. When the end faces are out of perpendicular, the optical axis assumes a certain angle relative to the extension of the center axis.

The lens element of the invention is ordinarily circular in cross section, but may be of polygonal and other forms, and the size and shape of the cross section may vary along the center axis without any accompanying drawbacks.

For an optical system to be composed of a plurality of lens elements according to the present invention, it will be most convenient to attach the end faces of the lenses with a transparent bonding agent having a given refractive index. And for the interposition of blank spaces in the combination of the inventive lens elements, an integral structure may be obtained by joining the end faces through a transparent rod-like member having a constant refractive index distribution.

The lens of the invention may have chromatic aberration due to dispersion as in ordinary optical lenses, but such a chromatic aberration can be reduced to a certain extent by combining with the lens of the invention a lens element having a different rate of dispersion and a negative coefficient (a) of refractive index gradient.

Since the instant optical lens element is permitted to function as a lens due to the distribution of refractive indexes in the interior, curvatures of the end faces need not be finished. According to the present invention, therefore, a grinder required conventionally for the production of prior curved optical lenses can be dispensed with and, moreover, lenses including those having less than several millimeters of aperture and also having a small aberration can be produced at extremely low cost.

Also, in the instant optical lens element, the focal distance can be varied only by changing its length in axial direction, so that lenses having different optical characteristics determined solely by their lengths can be obtained by cutting out lenses of different lengths from the same lens material having a certain refractive index distribution.

Furthermore, since the instant optical lens element is made of a solid transparent substance, a refractive index distribution once determined is maintained without fluctuation. As compared with conventional gas lenses which require the application of external power, are unstable, and are difficult to produce in small sizes, the lenses proposed by the present invention do not require the application of any'extemal force, are stable in performance, and small in size.

The lens element according to the invention can find a wide field of application in optical instruments such as microscopes, telescopes, other means for optical image transmission and various optical measuring devices.

The following Example 7 is based on the lens element according to FIGS. l4, l5 and 16.

EXAMPLE 7 A bar of. glass with a diameter of 0.5 cm. and consisting of wt. percent of K 0, 14 wt. percent of Na O,

7 wt. percent of 8,0; and 49 wt. percent of SiO, was immersed in a bath of thallium chloride at a high temperature for a given period of time, whereby a glass bar having a refractive index N at a center of 1.50, a surface refractive index of 1.57, and a refractive index distribution nearly satisfying the equation n N (l ar'), where r is a distance from a center and a 0.75 mm was obtained. This bar was cut to obtain columnar lenses with lengths, respectively, of 0.84 cm., 1.68 cm. and 2.45 cm. and whose end faces are planes so as to be perpendicular to their center axes. It was confirmed that these columnar lenses can function as concave lens with focal distances, respectively, of 4.5 mm., l.4 mm. and 0.54 mm.

In the following, relationship (that is, focal distance) between an object and its image will be described in detail in connection with the case in which n N (1 ar) is adopted.

When it is assumed that the constant (a) is .invariable in any cross section, the center axis is straight, both ends are in planes perpendicular to the center axis, then the relationship between an object and its image in the lens element according to this invention is as follows. in FIG. 17, the reference numeral 1 designates a columnar lens, having a radius R, a length t, and a refractive index distribution n N (l ar), where ar I.

The focal distance f of this columnar lens I can be obtained in the same way as in the case of equation (5).

More specifically, the focal distance f can be obtained by the following equation, when (2a)""" C:

However, the focal distance f is represented either by a distance measured toward a space on the object side from a first principal point of the lens or a distance measured toward a space on the image side from a secnd principal point. And, the distance h of a correspondingprincipal plane H as measured inwardly from end faces of the lens is represented by:

h (NC) tan ct In FIG. 17, F1 and F2 respectively designate the positions of focal points on the sides of the object and image, while H l and H2 represent principal planes on the sides of the object and image.

When an object P is placed at a position in a space on the side of the object at a distance k from the principal plane H] on the object of lens I, and, consequently, an image Q is formed at a position in a space on the side of the image at a distance I from the principal plane H2 on the image side of the lens, paraxial light-beams in this case are such that the equation K I f" is established between the distance k of the object and the distance [of the image, in the same way as in an ordinary lens formula.

Said equation (7) of the focal distance and the equation (8) of the principal plane distance h are shown in FIG. 18 as the functions of the length of the lens. The axis of abscissa in the graph plotted in the drawing represents the length of the lens, while the axis of ordinates represents the focal distance and principal plane distance. The full lines designate the focal distance f, and the chain lines represent the main plane distance it. The focal distance is varied in a range of (NC) to infinity, or (NC) to negative infinity, according to the length of the lens. When the length of the lens is limited to a range from (2C)1r (2m (5/3) to (2C)-rr [2m (1/3)], where m is a positive integer, the focal distance adopts values between (NC) and 2(NC) or between -(NC) and 2(NC)". Accordingly, a lens having a length in the above range can afford an extremely small focal distance. Furthermore, as is seen from the drawing, the lens has a focal point outside itself at a portion where the full lines f are higher than the chain lines h, that is, when the length of the lens adopts a value from FIG. 19 shows relative variation between the image and object when the position of the object is changed. When the object is moved from P1, P2 to P3 in the drawing, its image due to the lens I is changed from Q1, O2 to Q3. The parallel light beams from the object side, said beam being in parallel with the axis, are converged at one point at the position of the focal point F2. The parallel light beams from the image side are focused at a focal point Fl at a position symmetrical to the lens. When the object is moved from P1 to P2, an inverted real image is formed, increasing gradually as it moves from Q] to 02. When the object is moved to P3 located on the inner side of F1, its image becomes an erect virtual image 03.

Now, optical system of the case, in which center axis of the lens element according to the invention is bent, will be described hereinbelow. In this case, let it be assumed that the constant a is positive and all sectional areas of the same lens element, and both end surfaces of the element, are flat planes perpendicular to said center axis. In FIG. 20 (A), a lens element having a l4 shape resembling a curved cylinder having a length 1 along its center axis bent to a curvature U. This lens element has a radius R and a refractive index distribution represented by the equation n N (l ar as de- L LEQE JIEM" detail, rfifisi t $55192 to FIG. 20 (A), if a light beam near the center axis is considered in connection with the case where an object P is set at a front position on the extension of the center axis and an image Q in formed at rear position extended from the center line and the condition 2a C taken, thesame equations as the equations of through 9 in the case of lens element having straight center axis are established. Of course, however, the optical axis of the lens element does not coincide with the center axis of the lens element and deviates by a distance of (2aU) toward the outside. In FIG. 20 (A), the broken line h represents the center axis of the lens element and its extension and the chain line j represents the optical axis of the lens element and its extension. Furthermore, f, h, k and l in the equations 7, 8 and 9 are respectively distances measured along the optical axis and its extension.

Even when the curvature radius of the curve of the center axis of the lens is varied in the length direction of the lens, the relative positions of an object and image as well as magnification are the same as in the foregoing, and only an optical axis at the curved portion is shifted from the center axis. This state is shown in FIG. 20 (B), where the dotted line represents the part of the optical axis which is deviated from the center axis and the image of an object P is transmitted through a fibrous transparent substance 25 to form an image 0.

Now, considering'a case in which the lens element according to this invention has such a refractive index distribution that the constant (a) varies along its center axis, let it be assumed that axis Z is taken along the center axis, one end of the lens corresponds to Z O and the other end thereof corresponds to Z Zn, and a at an arbitrary portion corresponds to a (2). FIG. 21 plots the relationship between an object and its image on the assumption that the object is placed onto an end side where Z 0 of a lens element having such a refractive index distribution that a decreases with increase in Z for instance, a (Z) a (0) (1- Z), where X is a position constant and 22 1. FIGS. 22, 23 and 24 represent refractive indexes at cross section 22A-22B, 23A-23B, and 24A-24B in FIG. 21. The light-beam in the interior of the lens progresses while oscillating in its amplitude and wave length which are gradually increased, so that the lens can afford a higher degree of resolving power and higher magnification as compared with lenses having constant a. Desirably, the size of the cross section of a lens in which a decreases with increase in Z should be increased with the increase of Z because the brightness of an image obtained thereby can be augmented by preventing the impingement of light to the lateral side of the lens.

Both end faces of a lens element according to this invention have ordinarily a plane perpendicular to the center axis of the lens at its end. When the end faces are out of perpendicular, the optical axis of the lens comes to have a certain angle to the extension of the center axis.

The inventive lens element is ordinarily circular in cross section, but may be of polygonal and other forms, and the size and shape of the cross section may very 

1. A light beam transmitting transparent conductor consisting of an elongated optical transparent element having a refractive index distribution in Each cross-section perpendicular to the center axis of said element approximately satisfying the following relationship n N(1 - ar2) where N represents the refractive index at said center axis in any element crosssection, n represents the refractive index at a radial distance r from said center axis in said cross-section, and a is a positive constant in said cross-section, said transparent element having an input end face and an output end face each perpendicular to said center axis and having an optimum spot size at said input end face represented by the following formula Wo NOT = square root ( lambda /No pi ) .2 3/4 . ao 1/4 where Wo represents the optimum spot size at said input end face, lambda represents the wave length of a light beam to be transmitted through said transparent element, No represents the refractive index value N at said input end face, and ao is the value of a at said input end face, at least one of the factors N and a being such that the value thereof increases gradually from at least said input end face of said element toward an intermediate portion of said element along said center axis so that said element has an optimum spot size gradually increasing from said intermediate portion toward said input end face in such a manner that a light beam accurately introduced into said element upon said input end face with proper mode matching is transmitted axially through said element and exits therefrom at said output end face.
 2. A light-beam transmitting transparent conductor as claimed in claim 1 in which said element has a cross-sectional radius which increases from said intermediate portion toward said at least one end surface.
 3. A light beam transmitting conductor consisting of at least two sections disposed in end-to-end relationship to provide a long conductor, each of said sections consisting of a rod-shaped transparent element having a refractive index distribution in each cross-sections perpendicular to the center axis of said element approximately satisfying the following relation n N (1-ar2) where N represents the refractive index at said center axis in any element cross-section, n represents the refractive index at a radial distance r from said center axis in said cross-section, and a is a positive constant in said cross-section, each said transparent element having two opposite end faces each of which is perpendicular to said center axis and having an optimum spot size at one of its end faces represented by the following formula Wo Square Root ( lambda /No pi ) . 2 3/4.ao 1/4 where Wo represents the optimum spot size at said one end face, lambda represents the wave length of a light beam to be transmitted through said transparent element, No represents the refractive index value N at said one end face, and ao is the value of a at said one end face, at least one of said two elements having at least one of the factors N and a thereof gradually increasing from at least said one end face which is disposed adjacent an end face of the other of said to elements toward an intermediate portion of said one element along said center axis so that said at least one of said two elements has an optimum spot size which increases gradually from said intermediate portion toward said one end face in such a manner that a light beam exiting from an end face of said other element is accurately introduced into said one element upon said one end face with proper mode matching and is axially transmitted through said one element. 